In this paper we study the four-point correlation function of the energy–momentum supermultiplet in theories with N = 4 superconformal symmetry in four dimensions. We present a compact form of all component correlators as an invariant of a particular abelian subalgebra of the N = 4 superconformal algebra. This invariant is unique up to a single function of the conformal cross-ratios which is fixed by comparison with the correlation function of the lowest half-BPS scalar operators. Our analysis is independent of the dynamics of a specific theory, in particular it is valid in N = 4 super Yang–Mills theory for any value of the coupling constant. We discuss in great detail a subclass of component correlators, which is a crucial ingredient for the recent study of charge-flow correlations in conformal field theories. We compute the latter explicitly and elucidate the origin of the interesting relations among different types of flow correlations previously observed in arXiv:1309.1424.

High proportions of autistic children suffer from gastrointestinal (GI) disorders, implying a link between autism and abnormalities in gut microbial functions. Increasing evidence from recent high-throughput sequencing analyses indicates that disturbances in composition and diversity of gut microbiome are associated with various disease conditions. However, microbiome-level studies on autism are limited and mostly focused on pathogenic bacteria. Therefore, here we aimed to define systemic changes in gut microbiome associated with autism and autism-related GI problems. We recruited 20 neurotypical and 20 autistic children accompanied by a survey of both autistic severity and GI symptoms. By pyrosequencing the V2/V3 regions in bacterial 16S rDNA from fecal DNA samples, we compared gut microbiomes of GI symptom-free neurotypical children with those of autistic children mostly presenting GI symptoms. Unexpectedly, the presence of autistic symptoms, rather than the severity of GI symptoms, was associated with less diverse gut microbiomes. Further, rigorous statistical tests with multiple testing corrections showed significantly lower abundances of the genera Prevotella, Coprococcus, and unclassified Veillonellaceae in autistic samples. These are intriguingly versatile carbohydrate-degrading and/or fermenting bacteria, suggesting a potential influence of unusual diet patterns observed in autistic children. However, multivariate analyses showed that autism-related changes in both overall diversity and individual genus abundances were correlated with the presence of autistic symptoms but not with their diet patterns. Taken together, autism and accompanying GI symptoms were characterized by distinct and less diverse gut microbial compositions with lower levels of Prevotella, Coprococcus, and unclassified Veillonellaceae.